2020/01/13 by Craig, Andrew P. K., Gouveia, Maria J., Haviar, Miroslav · 1 citation
#06B15 #06B23 #06D50 #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2001.04182
In \citeCGH15 we introduced TiRS graphs and TiRS frames to create a new natural setting for duals of canonical extensions of lattices. In this continuation of \citeCGH15 we answer Problem 2 from there by characterising the perfect lattices that are dual to TiRS frames (and hence TiRS graphs). We introduce a new subclass of perfect lattices called PTi lattices and show that the canonical extensions of lattices are PTi lattices, and so are `more' than just perfect lattices. We introduce morphisms of TiRS structures and put our correspondence between TiRS graphs and TiRS frames from \citeCGH15 into a full categorical framework. We illustrate our correspondences between classes of perfects lattices and classes of TiRS graphs by examples.